Abstract

We produce simulations of the atomic CII line emission in large sky fields in order to determine the current and future
prospects for mapping this line during the high redshift epoch of reionization.
We calculate the CII line intensity, redshift evolution and spatial fluctuations using observational relations
between CII emission and the galaxy star formation rate (SFR) over the frequency range 200 - 300 GHz. We estimate
an averaged intensity of ICII=(4±2)×102Jysr−1 in the redshift
range z∼5.3−8.5. Observations of the CII emission in this frequency range will suffer
contamination from emission lines at lower redshifts, in particular CO rotational lines. Using simulations, we
estimated the CO contamination to be ICO≈103Jysr−1 (originating from galaxies
at z<2.5). Using detailed simulations
of the CII and CO emission across a range of redshifts, we generate maps as a function of angle and
frequency, fully taking into account this resolution and light cone effects. In order to reduce the foreground
contamination we find that we should mask galaxies below redshifts ∼2.5 with a CO(J:2-1)
to CO(J:6-5) line flux density higher than 5×10−22Wm−2 or a AB magnitude lower than mK=22.
We estimate that the additional continuum contamination originating in emission from stars and in dust, free-free,
free-bound and two photon emission in the ISM is of the order of 105Jysr−1 however it can be removed from observation
due to the smooth evolution of this foreground with frequency. We
also consider the possibility of cross correlating foreground lines with galaxy surveys in order to
probe the intensity of the foregrounds. Finally, we discuss the expected constraints from two experiments capable
of measuring the expected CII power spectrum.

Subject headings:

1. Introduction

The epoch of reionization (EoR) is a fundamental stage in the history of large scale structure formation.
The process of hydrogen ionization was fueled by radiation from the first galaxies which formed in overdense regions. Therefore, this process depends on a large set of astrophysical and cosmological parameters
(Venkatesan 2000).

There are already several experiments in operation using low frequency telescopes, such as the Murchison Widefield Arrays (MWA) (Tingay et al. 2013), the Giant Metrewave Radio Telescope (GMRT) (Paciga et al. 2011), the Precision Array for Probing the Epoch of Reionization (PAPER) (Parsons et al. 2010) and the Low Frequency Array (LOFAR) (Rottgering et al. 2006) aimed at constraining this epoch through the measurement of the 21cm signal. Future experiments such as Phase II of HERA 111http://reionization.org and the Square Kilometre Array low frequency instrument (SKA1-LOW) (Mellema et al. 2013) should push this measurement to even higher redshifts.

One of the main challenges for probing the EoR with the 21 cm line is that observations will be contaminated by foregrounds several orders of magnitude higher than the signal (Shaver et al. 1999). Although the frequency smoothness of these foregrounds provides a way to remove them (Santos et al. 2005; Chapman et al. 2012), the combination with calibration errors and systematics complicates the foreground cleaning process.

Independent ways to measure this signal and to probe the reionization process are therefore required in order to ensure the validity of our measurements related to reionization.

In this work we analyse the use of CII intensity mapping both to probe the EoR during its final stages and to confirm and complement the 21 cm data. Although not resolving individual sources, the intensity mapping technique has the advantage of measuring all the
emission in a given frequency band originating from a relatively large sky patch. This way, it is sensitive to radiation from faint sources and the diffuse IGM which at these high redshifts cannot be detected with other methods, but whose contribution to the total signal is often important (Gong et al. 2012; Silva et al. 2012). Compared to other techniques, intensity mapping has the advantage of providing three dimensional spatial information of the sources of emission that can be used to further understand the processes of structure formation. Intensity maps can also be used as cosmological probes since the fluctuations in the intensity of emission/absorption lines are correlated with the underlying dark matter density fluctuations (Carilli 2011). In particular, with CII, we can make maps of the sources of ionization, while the 21cm signal will simply be sensitive to the IGM.

We show the potential of CII intensity mapping by simulating mock observational cones of CII emission
and its foregrounds at frequencies from 200 GHz to 300 GHz, taking into account the light cone effects. This allows us to test possible ways to reduce the foregrounds without erasing the signal. The main foregrounds in CII intensity maps from the EoR will be contamination from other far-infrared emission lines from lower redshifts, in particular emission from CO rotational transitions. CO emission from normal galaxies at z>1 is poorly constrained by observations. Therefore, in order to properly estimate the intensity of these lines and the contamination power spectra relative to CII observations, we used two independent methods. First we used the simulated galaxies catalog from the SAX-Sky simulation which uses a phenomenological model to calculate the luminosities of different CO transitions (Obreschkow et al. 2009a). We then confirmed our predictions using IR luminosity functions (LFs) and other observational data to estimate the relative
intensities of the several CO transitions.

We find that CO contamination is dominated by bright sources and so it can be efficiently reduced by masking the pixels where radiation from these sources is observed. In order to apply this procedure we need a complementary experiment to measure CO emission from galaxies brighter than a given flux. This can be done with galaxy surveys targeting the CO emission, which would on its own be a powerful astrophysical probe on the conditions of the ISM. Alternatively the masking of the contaminant galaxies could be done with a CO tracer, easier to be observed, such as the SFR or the relative magnitude in a given filter.

We also explore
the possibility of cross correlating CII and 21 cm maps in order to obtain maps of the EoR that are clean from foregrounds and systematics. This is possible since two lines
emitted from the same redshift will be observed at different frequencies and so they will be contaminated mainly by uncorrelated foregrounds (Gong et al. 2012).

This paper is organized as follows: In Section 2 we describe how to theoretically estimate the CII emission. In
Section 3 we describe the CII foregrounds. In Sections 4 and 5 we describe how we used simulations to generate the signal and the foregrounds. In the 5th Section we present the parameters of an experiment able to measure the CII signal and the CO signal in the 200 GHz to 300 GHz band and in Section 6 we discuss how to remove the CII foregrounds. We conclude with a discussion of the results obtained in Section 7.

2. Calculating CII emission

CII emission is originated in i) the interstellar medium (ISM), ii) Photodissociation regions (PDRs), iii) ionized regions (HII regions), iv) cold atomic gas or v) CO-dark molecular gas (regions in the boundary of molecular clouds with H2 but without CO gas). Observations of the relative intensity of different emission lines have shown that the main source of CII emission is the dense PDRs located in the boundary of HII regions. PDRs are dense and warm regions of the ISM located between HII regions and molecular clouds. They contain mostly neutral gas, but due to their proximity from O, B stars or AGNs the physical and chemical properties of the gas are set by the strong far ultraviolet (FUV) field. The strong FUV to X-ray radiation that penetrates the PDR is absorbed by dust grains which emit electrons heating the gas, or by atoms with an energy threshold for ionization below the Lyman alpha limit such as carbon, oxygen and nitrogen. The FUV also causes
transitions from atomic to molecular hydrogen and from ionized carbon to carbon monoxide (Hollenbach & Tielens 1997).

CII photons are emitted in PDRs as a cooling mechanism and so they are a consequence of pre-existing heat. CO-dark clouds are envelopes of dense H2 gas with densities too low for carbon to be converted to CO, but which can be identified by their CII emission. The contribution from CO-dark clouds to the total CII budget is not yet clear but recent studies of our galaxy indicate that it can be high (up to ∼28%) (Pineda et al. 2013) under certain astrophysical conditions, more characteristic of the low redshift universe. Diffuse cold atomic gas can be characterized by its emission in the hydrogen 21 cm line and in the CII line. The intensity of emission in this gas phase will be proportional to the collisional rate which depends on the gas density and temperature and therefore also on FUV strength.

The carbon ionization energy is only 11.3 eV which is less than the 13.6 eV necessary to ionize hydrogen so at first we could expect, as was done in Gong et al. (2012), that all the carbon in HII regions would be ionized. There would then be a high emission in the CII 157μm line since its excitation potential is only of 91 K. Under this assumption most of the CII emission would come from the highest density locations inside HII regions. However this is not supported by observations: several observational maps of the spatial distribution of CII emission in galaxies indicate that the CII emission is mainly originating in PDRs and that HII regions contribute only a few % of the total CII emission (Lebouteiller et al. 2012; Rigopoulou et al. 2014). There are studies which indicate a contribution from
HII regions that can reach up to 30% of the total CII emission (Carral et al. 1994; Stacey et al. 1999; Aannestad & Emery 2003; Rigopoulou et al. 2013). However, these studies point out that most CII emission is originated in the low density HII regions. The more simple explanation for this unexpected result is that the carbon in the more dense places in HII regions is highly shielded from radiation by hydrogen and so almost all of the ionized carbon is located in low density regions.

The Herschel telescope and the SOFIA observatory were used to observe typical tracers of PDRs, HII regions and
other galactic regions (Kaneda et al. 2013) and these observations showed that CII emission has a more
complex spatial structure than most other infrared lines. In order to properly estimate the CII
emission from a galaxy, it is necessary to observe it with high spatial resolution, which is not possible for most distant galaxies. Alternatively we can use the intensity mapping technique to measure the integrated CII emission from many galaxies.

2.1. Theoretical formulas to estimate CII emission

The intensity of CII emission is given theoretically (Gong et al. 2012) as:

Iν=hc4πH(z)(1+z)3AulfgrdCIInCII(z)×

(1)

guglexp(−T⋆,ul/TS,ul)[1−exp(T⋆,ul/TS,ul)−1(2hν3/c2Iν)νul],

where fgrdCII is the fraction of CII ions at the ground level 2P1/2, nCII is the number
density of once ionized carbon atoms, H(z) is the hubble parameter, TS
is the spin temperature and T⋆≡hνul/kB (where νul is the frequency of the transition).
The statistical weights are gu=4 and gl=2 and the Einstein spontaneous emission coefficient
is Aul=2.36×10−6s−1.

As many of the parameters in Equation 1 are poorly known and cannot be directly obtained from observations we use an alternative formula, based on the halo model, to obtain the intensity of a line emitted from several galaxies in a relatively large volume. For this we made the simplification of assuming that the average luminosity of each of these galaxies is only a function of the mass of the dark matter
halo which contains it and at most its redshift. The average intensity of a line is then given by:

¯I(z)=∫MmaxMmindMdndML(M,z)4πD2Ly(z)D2A

(2)

where dn/dM is the halo mass function (Sheth & Tormen 1999), M is the halo mass,
Mmin=108M⊙, Mmax=1014M⊙, DL is the proper luminosity distance,
DA is the comoving angular diameter distance and y(z)=dχ/dν, where χ is the comoving distance
and ν is the observed frequency.
The relation between LCII and the halo mass is physically based in the dependence of LCII in the
number density of CII atoms which should be proportional to the halo mass.

2.2. Calculating CII emission using observational based relations

The CII luminosity of a galaxy can be estimated from other observable quantities as long as there is a reasonable
correlation between the two. For large volumes, since we integrate over several galaxies, it is even more reliable to use these observational relations to estimate the overall luminosity from these regions.
CII emission is powered by FUV radiation and so there is a correlation between these two quantities which can be
converted to a relation between CII and FIR luminosities given that in the star forming galaxies (which will dominate the signal) there is a known correlation
between the FUV and FIR fluxes.
The CII luminosity of a galaxy also depends on other astrophysical properties of the galaxy such as its
metallicity, however the average ratio R=LCIILFIR for nearby,
late type galaxies and for 108L⊙≤LFIR≤1010.5L⊙ is approximately
constant (Boselli et al. 2002) and is given by:

LCII(M,z)[L⊙]=0.003×LFIR.

(3)

This relation is also consistent with recent observations of high redshift galaxies (Stacey et al. 2010)
and with observations of ULIRGS (LIR>1011.5L⊙),
where a ratio of R=(0.8−4)×10−3 in the CII to FIR luminosities was found (Rigopoulou et al. 2014).
In PDRs the same ratio is inversely proportional to the strength of the
ambient radiation field G0, since LFIR is proportional to G0 and LCII depends weakly on G0(Kaufman et al. 1999). Therefore, this ratio is likely to slightly increase to low mass galaxies
(up to R∼0.01) and to decrease to high mass galaxies.
The IR and the FIR luminosities are connected by the following relation:

The integrated IR
luminosity, LIR=L(8−1000μm) is related to the galaxies star formation rate (ψ) by the Kennicutt (1998) relation:

(5)

Using Equations 3, 5 and 4 we obtained the following relation
between CII luminosity and SFR:

LCII(M,z)[L⊙]

=

0.003×LFIR[L⊙]

=

0.003×0.53×LIR[L⊙]

=

9.22×106ψ(M,z)[M⊙/yr].

The connection between CII luminosity and the SFR can be easily understood in the case of CII emission arising
from warm photodissociating regions, since in this case the FUV radiation ionizes the carbon in the outer
layers of the photon-dominated molecular clumps which, in its turn emits CII with a luminosity proportional to the
FUV flux which is linked to the galaxy SFR (de Looze et al. 2011). In HII regions the amount of ionized carbon should
increase with the size of the region, which is proportional to the stellar radiation UV intensity. However, given that not all carbon is necessarily ionized at the same time in HII regions and that the CII luminosity of these regions also depends on the astrophysical conditions of the gas, one expects a considerable dispersion in the relation between CII luminosity from HII regions and the SFR.
Alternative relations between the CII luminosity and the SFR, obtained using different
galaxy datasets and using a SFR estimated from the infrared luminosity or from the Hα luminosity, can be found for example in Boselli et al. (2002), de Looze et al. (2011) or Sargsyan et al. (2012).
All of the referred observational studies indicate that the ratio between CII and SFR is smaller for ultra-luminous
galaxies although these galaxies account for no more than a few percent of the total emission, which justifies our use of a constant ratio.

Figure 1.— Left panel: Star formation rate versus halo mass for redshifts 6 (red upper lines) and 8 (blue upper lines). The dotted
lines show the relations taken from the Guo et al. (2011) galaxies catalogue for low halo masses, the
dashed lines show the relation taken from the De Lucia & Blaizot (2007) galaxies catalogue for high halo masses at
the same redshifts. The solid lines show the parameterizations from Equation 8. Right panel: Star formation rate
density from the simulations (black solid line), obtained by integrating Equation 8
over the halo mass function. The green circles mark the SFRD corresponding to the UV luminosities corrected
for dust extinction from Bouwens et al. (2011). The red and blue circles were obtained with measurements of
gamma-ray bursts by Kistler et al. (2013) and Robertson & Ellis (2012), respectively.

The first five observations of star forming galaxies at z≃6.5 detected by the ALMA experiment were published
(see eg. Wang et al. (2013)). These galaxies have upper limits for the CII luminosity below what is
predicted by Equation 2.2. However, their SFRs are above 10M⊙yr−1 which puts them in the
region where a CII deficit was already expected. Observations of typical star forming galaxies at z∼5−6, recently
obtained with ALMA, show CII luminosities versus FIR ratios clearly above the usual values at z=0 (Capak et al. 2015).
Also, for intensity calculations, according to our model, galaxies with SFRs above 10M⊙yr−1 only represent
around 20% of the total CII intensity and so when fitting the CII luminosity versus SFR relation in observational data we should
take into account that less intense galaxies (which are too faint to be observed especially at high redshifts) have a large weight
in the CII intensity and that they are more likely to have a more robust LCII/SFR ratio.

In order to obtain upper and lower bounds to our CII intensity estimation we decided to use 4 models for the
LCII versus SFR relation, to which we will refer to as: m1, m2, m3 and m4. While
Equation 2.2 corresponds to parameterization m2, parameterization m1 corresponds to the recent fit to high redshift galaxies by De Looze et al. (2014) and parameterizations m3 and m4 correspond to fits to the galaxies in Figure 4. These models can all be parameterized as:

Here the CII intensity was estimated using Equation 2 with a CII luminosity given by Equation 7,
converted into a CII luminosity versus halo mass relation. The conversion between SFR and halo mass was made using simulated
galaxy catalogs post-processed by De Lucia & Blaizot (2007) and Guo et al. (2011) from the Millennium and Millennium II dark matter simulations (Springel et al. 2005; Boylan-Kolchin et al. 2009).
We did not use an observational based relation since such a relation is not available for low halo masses and high redshifts. The galaxy SFR from the simulated catalogs is on average related to the mass of the dark matter halo containing the galaxy by:

ψ(M,z)=M0×(MMa)a(1+MMb)b,

(8)

where the values for the parameters M0, Ma, Mb, a and b are available in Table 2 for
redshifts lower than 20. The evolution of the SFR with mass can be seen in the left panel of Figure 1 for redshifts
6 and 8.

Redshift range

M0

Ma

Mb

a

b

0.00-00.50

10−8.855

1.0×108

8.0×1011

2.7

-4.0

0.00-02.75

10−9.097+0.484×z

1.0×108

8.0×1011

2.7

-4.0

2.75-03.25

3.3×10−8

1.0×108

4.0×1011

2.7

-3.4

3.50-04.50

1.5×10−7

1.0×108

3.0×1011

2.6

-3.1

4.50-05.50

9.0×10−7

1.0×108

3.0×1011

2.4

-2.3

5.50-06.50

3.6×10−6

1.0×108

2.0×1011

2.25

-2.3

6.50-07.50

6.6×10−6

1.0×108

1.6×1011

2.25

-2.3

7.50-09.00

1.0×10−5

1.0×108

1.7×1011

2.25

-2.4

9.00-11.00

3.7×10−5

1.0×108

1.7×1011

2.1

-2.2

11.00-13.00

5.0×10−5

1.0×108

1.5×1011

2.1

-2.2

13.00-20.00

[5.0+(z−13.0)]×10−5

1.0×108

[1.5+(z−13)×0.015]×1011

2.1

−2.2−(z−13)×0.03

Table 2SFR parameters based in the average relations from the simulated galaxy catalogs

The use of this formula results in the star formation rate density (SFRD) evolution shown in the right panel of Figure 1 assuming a dark matter halo mass range from 108M⊙ to 1014M⊙.
The Millennium and Millennium II simulations only goes till a redshift of 20. However unless we want to consider unusual stars
the relation for z=20 should be a good approximation for z>20, if required.

2.3. Calculating CII emission using gas physics

The maximum possible upper value for the CII emission can be obtained assuming that all the carbon in the hot gas
(typical HII regions) in a galaxy is ionized and therefore emitting in the CII line, such as was done in
Gong et al. (2012).
Here, we do a similar calculation but with an improved parameterization of the metallicity in the galaxies hot gas
obtained using the Guo et al. (2011) galaxies catalog for low mass halos and the De Lucia & Blaizot (2007)
galaxies catalog for high halo masses.
The resulting relation between halo mass and metallicity in the hot gas component is shown in Figure 2. By
analysing this figure we found that the metallicity in the lower mass halos of the De Lucia & Blaizot (2007)
simulation is lower than the one found in the halos from the Guo et al. (2011) simulation, although these
simulations used very similar prescriptions to determinate the galaxies metallicity. Since the Guo et al. (2011)
simulation has a much higher mass resolution, we believe that their results are more reliable for the low luminosity halos, since the halos in the De Lucia & Blaizot (2007) galaxies catalog are only well resolved for masses above 3×1010M⊙.

Figure 2.— Mass in metals in the hot gas component MZ as a function of the halo mass M at z≈7. The
dahed dotted line shows the mean
relation from the (Guo et al. 2011) galaxy catalog, the dashed line shows the mean relation from the
(De Lucia & Blaizot 2007) galaxy catalog and the solid line shows our fits to the mean values. The dots show
the dark matter halos in the two catalogs.

The average relation between MZ and halo mass M in the referred simulated galaxy catalogs can therefore, be parameterized in the form:

MZ(M)

=

M0(M/Ma)a(1+M/Mb)b

×

where at the redshift range 5.0 to 8.5 these parameters take the values:
M0=z−1, Ma=1.0×108M⊙, Mb=9.0×109M⊙,
Mc=2.0×1012M⊙, Md=2.0×1013M⊙, a=1.7, b=1.0, c=−5.0 and d=2.5.

Assuming that all the carbon in the hot gas is ionized and that the carbon mass corresponds to a fraction of
21% of the total mass in metals (this is the same percentage of carbon found in the sun) we obtain
MCII=0.21MZ. In reality only a fraction of the carbon in HII regions is ionized which can be easily included
in these calculations.
At large enough volumes the number density of CII atoms can be estimated from the halos mass using the formula:

nsimCII(z)=∫MmaxMmindMdndMMCII(M,z)mc,

(10)

where mc is the atomic carbon mass.

We can obtain an upper value for the intensity of CII emission in HII regions by replacing in Equation 1 the
CII number density obtained from Equation 10. We estimated the CII number density by assuming that HII regions have an
electronic temperature of 104 K and an electronic density of 104cm−3 (these values correspond to saturation emission values as obtained in Gong et al. (2012)).

Figure 3.— CII intensity as a function of redshift according to the CII models m1, m2, m3 and m4 (upper to lower
solid lines). The cyan dashed
line corresponds to the CII luminosity from HII regions (assuming that all the carbon is ionized).

In Figure 3 we show the CII intensity estimated assuming several models for the CII emission. The average
intensity of CII emission in the redshift range shown is between
¯ICII≈6×102Jysr−1 for model m1 and
¯ICII≈9×101Jysr−1 for model m4. The average CII intensity, obtained by averaging
models m1 to m4, between z∼5.5 and z∼8.5 is ¯ICII≈4±2×102Jysr−1.

In Figure 4, the CII luminosity as a function of the SFR for the different methods
described, is shown together with observational points of normal local galaxies from Malhotra et al. (2001)
and with observational upper limits for high redshift galaxies. The
observed high redshift galaxies, presented in this figure, have high SFRs which indicates that they are
very massive and rare or that they have extreme SFRs/Mass ratios. In either
case these galaxies have little effect on the overall CII intensity.

Figure 4.— CII luminosity as a function of the SFR. The cyan dashed
line corresponds to the CII luminosity from HII regions (assuming that all the carbon is ionized) and the solid
lines corresponds to the CII luminosity obtained from the SFR using relations m1, m2, m3 and m4
(upper to lower lines).
The red dots are local universe galaxies from the ISO Key Program (Malhotra et al. 2001) and
the other symbols are upper limits from galaxies at z>6.5
(taken from: (González-López et al. 2014; Kanekar et al. 2013; Ota et al. 2014)).

The CII luminosities from ionized regions, presented in Figure 4,
were obtained by assuming that LCII is linearly proportional to the halo mass and by determining the constant of
proportionality between the two by imposing that Equations 2 and 1 give the same result. The
relation between halo mass and SFR was assumed to follow Equation 4.

3. CII Foregrounds

The CII line emitted in the redshift range z ≈ 8.51 - 5.35 is observed at frequencies
200−300GHz. CII is a far-infrared line and so CII intensity maps will be contaminated by other infrared lines
and by infrared continuum emission from galaxies and from the IGM. In this section we show estimations for the contamination from all of these extra-galactic sources in the relevant observing frequency band. In addition we also consider contamination due to emission from our galaxy.

3.1. Contamination from line emission

The main contaminants in CII intensity maps will be emission lines from lower redshifts namely the [OI]145μm, the
[NII]122μm,
the [NII]205μm and the CO rotation lines from transitions CO(2-1) and higher.
The [OI]145μm and the [NII]205μm lines are typical of PDRs while the [NII]122μm line
is typical of HII regions and so the SFR can be used to roughly estimate their intensity of emission such as in the CII case (see: section 3.5).
The CO lines are emitted from molecular gas and their luminosities depend on several characteristics of the gas
and so we carefully estimate their intensity of emission in the next section.

3.2. CO signal from simulations

CO rotation lines will be the main contaminants in CII intensity maps observed at
frequencies 200 − 300 GHz. Since the luminosities of the several relevant CO transitions are poorly constrained observationally, we estimate
their intensities using the CO fluxes in the simulated galaxy catalog from Obreschkow et al. (2009a) and confirm
our results with a CO intensity calculated using only observational relations, when available.
The Obreschkow et al. (2009a) catalog is available for halo masses above 1010M⊙ and provides astrophysical properties such as the CO fluxes for rotational transitions (1-0) to (10-9). The CO emission was estimated from the galaxies molecular gas content and from the ISM temperature using physically based prescriptions
and assuming thermal equilibrium.

Each CO rotation line that is observed in the frequency range 200 - 300 GHz will come from the redshift range shown
in Table 3. Note that for the CO(2-1), as is shown in Table 3, the minimum relevant redshift for this study
is zero which corresponds to the line rest frequency.

where the sum in J (angular momentum) is a sum over the luminosities of the different rotation lines from CO(2-1) to CO(6-5)
and z=νJCO/νo−1.
We do not account for higher CO transitions since according to this CO model the CO contamination in CII intensity maps is highly dominated
by the lower CO transitions.
We also justify
our choice by arguing that the contamination from transitions (7 - 6) and higher is originated from high
redshifts (4.8>z>1.7) and so the lower metallicity of these galaxies is likely to result in a considerably low CO emission.

Using the simulated fluxes we parameterized the CO luminosity of galaxies as a function of halo mass for transitions
CO(2-1) to CO(6-5) as:

LJCO(M)[L⊙]

=

L0×Md0×(1+MMc1)d1

×

(1+MMc2)d2(1+MMc3)d3(1+MMc4)d4,

where the parameters for each transition can be found in Table 4. Note that these parameters were obtained for each transition
by averaging the CO luminosity in the redshift range shown in Table 3.

Figure 5 shows the luminosity of the CO(2-1) transition as a function of halo mass, in the redshift range 0 to 0.15, obtained from the simulation.

Figure 5.— Luminosity of the CO(2-1) transition as a function of halo mass for the redshift band z∼0−1.5. The black dots correspond to halos
in the Obreschkow et al. (2009a) simulation. The blue dots show the mean of the scatter when binned in 30 logarithmic intervals in mass. The solid green
lines show the ±1σ relation. The red solid line corresponds to the parameterization given by Equation 3.2 with the
parameters from Table 4.

Given that the minimum halo mass available in the Obreschkow et al. (2009a) galaxy catalog is not low enough for our study, we extrapolated the average CO luminosity
to lower halo masses assuming that it is proportional to SFR at low masses.
The CO luminosities were parameterized as a function of dark matter halo masses and not as a function of galaxy masses
and therefore for high halo masses they include the contribution from a main galaxy and several satellite galaxies.
This parameterization could also have been made as a function of IR luminosity or SFR, however, galaxies powered by active
galactic nuclei have relatively small IR luminosities, small SFRs and high CO fluxes and so this population
would have to be taken into account separately.

Figure 6.— CO luminosity functions based on the Obreschkow et al. (2009a) CO model (dashed lines) and
on the observational CO model (solid lines) at redshifts
0 (left panel) and 1 (right panel). The yellow and green regions show the uncertainty in the CO observational model due only
to the uncertainty in the conversion factor between IR luminosity to CO(1-0) luminosity. The upper curves correspond to the
transition CO(2-1) and the lower curves correspond to transition CO(1-0)

The theoretical average power spectra of CO contamination presented in Figure 7 for transitions
CO(2-1) to CO(6-5) indicates that the dominant contamination will be due to the
low-J CO transitions. However, the ratios of different CO lines were obtained by assuming a simple model with a single gas
component in local thermodynamic equilibrium. This does not necessarily have to represent well the molecular gas conditions in all types of galaxies. A more recent work described in Lagos et al. (2011) and Lagos et al. (2012), attempts to estimate the luminosity of the several CO transitions using an improved method to estimate the molecular gas content in galaxies. This is based in a somewhat more detailed model of the gas properties, as compared to Obreschkow et al. (2009a), used to estimate the relation between CO emission and molecular gas content.
The main difference in the results obtained by these two authors is that the Lagos et al. (2012) model
predicts a smaller molecular content
in galaxies for z>2 and higher ratios between the CO luminosities for higher transitions.
These two corrections practically compensate themselves in terms of contamination in CII maps at the relevant
frequencies for these study and so they should not have a significant effect in the validity of our predictions for
intensity mapping. Even though there are limitations to the CO luminosities calculation made by Obreschkow et al. (2009a), observationally
only the CO(1-0) line is well constrain at small redshifts (z≤1) and in that case the CO LFs derived from the simulated
galaxies catalog are compatible with observations. The few CO observations at z>1 suggest a number density of CO
emitters higher than what is predicted by the Obreschkow model (Daddi et al. 2010; Tacconi et al. 2010; Aravena et al. 2012),
however these observations are restricted to mainly the CO(2-1) transition from very high luminosity galaxies while for the relevant
observed frequency range the CO emission is originated at z<1, where the models are in better agreement.

3.3. CO signal from observations

An observational only based model to estimate the CO(1-0) luminosity is presented in Sargent et al. (2013) and so to support our conclusions we used this completely independent model to estimate the CO contamination in CII maps. The Sargent model estimates CO emission from a recent IR luminosity function at z=1 presented in Sargent et al. (2012) and with the observational relations between IR and CO luminosities presented in Sargent et al. (2013).
The luminosity function (LF) is an useful way to put constraints on the overall luminosity of observed galaxies above a given
luminosity limit characteristic of each survey. It corresponds to the number density of galaxies per luminosity interval as a function of luminosity. The LF is commonly plotted in units of number density per decade in luminosity (Φ[Mpc−3dex−1], where dex accounts for the logarithmic variation of the luminosity for the bin used
(log10Lf−log10Li).
The Sargent IR LF for z≠1 can be scaled with redshift using the factor (1+z)2.8 in the galaxies luminosity and
scaling the number density as Φ∝(1+z)−2.4 for z>1.0 (for lower redshifts the number density is fixed).

The CO luminosities can be obtained from the IR LF using:

log(L′CO(J=1→0)Kkms−1pc2)=α1+β1log(LIRL⊙)

(13)

where (α1,β1)=(0.18±0.02;0.84±0.03) for normal galaxies and
(α1,β1)=(−0.28+0.15−0.09;0.84±0.03) for starbursts (Sargent et al. 2013).
In Figure 6 the CO LF based in the Obreschkow et al. (2009b) model was obtained using a halo mass function and the CO luminosity parameterization from Equation 3.2. The two models shown in Figure 6 agree taking
into account the uncertainty in the relation between the IR luminosity and CO(1-0) luminosity used in the observational CO model (showed as shaded regions). The uncertainties in the Sargent CO LFs are even higher if we take into account the error bars in
the IR luminosity function, or the uncertainty in the passage from the CO(1-0) line to higher transitions.

Ratios between the luminosities of the CO(1-0) line and higher CO transitions (in units proportional to the surface
brightness L′CO[Kkms−1pc2]) for
different types of galaxies are available in Carilli & Walter (2013). In order
to obtain observationally only based estimations for the LFs of the relevant CO transitions we used the Sargent
CO(1-0) model plus the Carilli & Walter (2013) observational ratios: r21=0.85, r31=0.66, r41=0.46
and r51=0.39 which are appropriate for submillimeter galaxies. Since there is no
available observational relation between transitions CO(6-5) and CO(1-0), we assumed that r61=r51.
For each transition the CO luminosity in [L⊙] can be obtained using:

LCO=3×10−11ν3L′CO.

(14)

Figure 7.— Power spectra of CO line emission made using the parameterization from Equation 3.2 in the frequency range 200 GHz to 300 GHz projected to the redshift of the CII line. The top solid line shows the
total CO power spectra and the lower lines show the CO(2-1) to CO(6-5) transitions.Figure 8.— Power spectra of CO line emission made using the observational CO model in the frequency range 200 GHz to
300 GHz projected to the redshift of the CII line. The top solid line shows the total CO power spectra and the lower
lines show the CO(2-1) to CO(6-5) transitions.

We will from now on refer to the observational CO luminosities predicted using the Sargent CO(1-0) LF plus the Carilli
et al. ratios for CO transitions as the observational CO model.
The main differences between the two CO models lies in the conversion
ratios between the luminosity of the several transitions given that the average ratio in the Obreschkow simulation are
r21=0.93, r31=0.70, r41=0.38, r51=0.12
and r61=0.02
at a redshift close to zero and slightly increase for higher redshifts. The flux ratios in the Obreschkow simulation
are appropriate for regular galaxies, while for star bursts and quasars the ratios between fluxes of high CO transitions are much higher.
Recent observationally based ratios for different CO transitions as a function of redshift can be found in Daddi et al. (2014). This study suggests
that the relative contribution from high CO transitions relevant for our study is even smaller than what is predicted by the two models discussed here. That is, it should be easier to remove CO contamination from observational maps.
Given the lack of observational measurements of fluxes of high CO transitions in normal galaxies, with masses below 1012M⊙, the ratios
between different CO transitions and the LFs from these lines are poorly constrained and this work can serve as motivation to plan an experiment especially designed to measure CO emission from several rotational transitions and their redshift evolution.

3.4. CO signal: intensity and power spectrum estimates

We will now show theoretical estimates for the intensity and the power spectra of CO contamination using the LFs obtained with
the two CO methods. The CO intensity can be obtained by integrating over the CO LF for the luminosity range available for each line. Following Gong et al. (2012) the CO intensity is given by:

IJCO(ν)=∫LJminLJmaxdLdndLLJCO4πD2Ly(z(ν,J))D2A,

(15)

where dn/dL=Φ(L).

When calculating the power spectrum from a CII map contaminated by CO emission, the corresponding CO power spectrum will be rescaled from
the original value at the CO emission redshift, both in amplitude and in terms of the wavelength.
Following Gong et al. (2014) the contamination CO power spectra is given by:

Pobs(k⊥,k∥)

=

[PclusCO(zf,J,kf)+PshotCO(zf,J,kf)]

(16)

×

⎛⎝[χ(zs)χ(zf)]2[y(zs)y(zf)]⎞⎠,

where the clustering power spectra is given by:

PclusCO(zf,J,kf)

=

¯I2f(zf)b2f(zf)Pδδ(zf,kf).

(17)

The indexes s or f indicate whether we are referring to respectively the source
(CII) or the foreground (CO) redshifts, χ is the comoving distance,
|→kf|=[(rs/rf)2k2⊥+(ys/yf)2k2∥]1/2 is the three dimensional k vector at
the redshift of the foreground line, Pδδ is the matter power spectra and bJCO is
the bias between the CO(J→J−1) signal and dark matter.

The shot noise power spectra due to the discrete nature of galaxies is given by:

PshotCO(z,J)=∫MmaxMmindMdndM[LJCO(M,z)4πD2Ly(z,J)D2A]2.

(18)

There are distortions in the observed power spectra in different directions due to redshift evolution of the
signal. In theory these distortions could be used to differentiate between the signal and the foregrounds or to
confirm if the foregrounds where effectively removed since in that case there should be no distortions observed (besides the known redshift-space distortions).
However, in practice this would require an experiment with an extremely high resolution and so in this study we
will only consider the spherical average power spectra. The foreground lines will contaminate the spherical
average CII power spectra at
|→ks|=[k2∥+k2⊥]1/2.

Since we assume that there is a correlation between CO luminosity and dark matter halo mass then the bias between the overall CO emission and the underlying dark matter
density field can be estimated from the halo bias (b(z,M)) as:

bJCO=∫MmaxMmindMdndMLJCO(M,z)b(z,M)∫MmaxMmindMdndMLJCO(M,z)

(19)

where Mmin=M(LJmin), Mmax=M(LJmax) and
LJCO(M,z)∝MαCO. The correct value for αCO changes with the
galaxy mass, assuming the values from the galaxies in the Obreschkow simulation we have αCO=1.5±0.5
for halos with M<1012M⊙ and αCO<1 for higher mass halos. For the
observationally based CO contamination power spectra we assume αCO=1 in
our calculations.
The estimated contamination power spectra of CO emission in CII maps observed in the frequency range
200 GHz to 300 GHz is shown in Figures 7 and 8 for respectively the Obreschkow CO model
and the observational CO model.

3.5. Contamination from atomic emission lines

The [OI]145μm, the [NII]121.9μm and the [NII]205.2μm atomic emission lines are emitted from PDRs or
from HII regions and so the luminosity of these lines is powered by stellar emission. Therefore it is expected to be
correlated with the galaxies SFRs.
The luminosity of these lines depends highly on the galaxies gas density and FUV flux (Kaufman et al. 1999). However, for a
large number of galaxies, their luminosity densities scale with the FIR luminosity. We therefore used the observational ratios, presented
in Table 5, taken from
(Graciá-Carpio et al. 2011; Brauher et al. 2008; Ferkinhoff et al. 2011; Zhao et al. 2013), to estimate the lines luminosities ([x]/[FIR] stands for the average fraction of FIR emission of each line).
The luminosity of these lines as a function of halo mass was then obtained using Equations 4, 5
and 8.
The intensity of each line in the relevant range of 200 to 300 GHz, estimated using Equation 2 is shown in Table 5.

line

[x]/[FIR]

z[200GHz]

z[300GHz]

Intensity

[OI]145μm

0.05%

9.3

5.9

5.1

[NII]122μm

0.01%

11.3

7.2

5.5

[NII]205μm

0.03%

6.3

3.9

58

Table 5Average intensity of several emission lines in the observed frequency range 200 - 300 GHz in units of
[Jysr−1].

The average contamination from these lines is considerably below the CII intensity.

3.6. Contamination from continuum emission

The contamination from continuum emission can be estimated from the SFR and gas properties.
The origins for the continuum emission considered here include: stellar continuum emission which escapes the galaxy, stellar emission
reprocessed by the dust in the galaxy, free-free and free-bound continuum emission caused by interactions between free electrons and
ions in the galaxies, and two photon emission originated during recombinations.
Since continuum radiation (with the exception of some bands in stellar continuum radiation) observed in the frequency range 200 - 300 GHz will be
emitted in the infrared band, it will not be absorbed by any of the main hydrogen lines or by
dust and so we can assume that this radiation is not affected during its path towards us.

The intensity of contamination from all of the referred continuum sources of infrared emission is shown in Table
6 and the detailed calculations are presented
in the appendix.

Source of emission

I(300GHz)

I(200GHz)

dust

3.0×105

2.0×105

stellar

4.1×10−3

8.5×10−1

free-free+free-bound

1.3×101

0.9×101

2-photon

3.4×10−12

2.8×10−12

Table 6Intensity of continuum emission observed at frequencies of 300 GHz and 200 GHz in units of [Jysr−1]

It is also expected that there is some contamination from the Milky Way which can be estimated from temperature maps
of our galaxy for the relevant frequencies. Using temperature maps from Planck at frequencies 143GHz, 217GHz and 353GHz
we estimated that unless we were in the center of the Milky Way where the brightness temperature can reach 0.2 - 0.3 K, the
average brightness temperature is well below 0.1K which corresponds to an observed intensity of 2.44×10−32Jysr−1 to
1.18×10−32Jysr−1 for 200 GHz and 300 GHz respectively.

The intensities in Table 6 show that the continuum contamination is above the CII signal
however continuum emission can be fitted and efficiently subtracted from the observational maps.

4. Simulations of the observed signal

The CII mock observational cone was made using the following steps:

A dark matter density field with a size of Lbox=634h−1Mpc and a number of cells of
N3box=18003 was generated using the
Simfast21 code (Santos et al. 2010; Silva et al. 2012).

The same code was used to generate dark matter halo catalogs from the previously
generated density field using the excursion set formalism and by sampling the halos directly from the density field. These
catalogs were made for redshifts 5.3 to 8.5 with
a redshift step of 0.1 and a halo mass range of 108M⊙ to 1015M⊙. At this point the halo
properties contained in the catalogs included only the halo mass and its position in a three dimensional box with the size
and resolution of the density field.

We randomly assigned astrophysical properties, such as SFR, from the
De Lucia & Blaizot (2007) galaxies catalog, to the generated
halos according only to the halos mass and redshift.

We added CII luminosities to the halo properties using the halos SFR versus CII luminosity relations
shown in section 2.1, which resulted in four CII luminosity values for each halo, one for each
of the m1, m2, m3 and m4 models.

In order to build the observational cones we made a box with 50 by 2562 cells which
covers the frequency range 200 to 300 GHz and the 1.3deg×1.3deg field of view with steps of respectively
dfo= 2 GHz and dang=8×10−3deg. The angular
coordinates correspond to positions in right ascension (RA) and declination (DECL), where
the center of the box (the cone rotation axis) is at RA = 0 and DECL = 0.

We filled the box with the halos by assuming that the halos z direction corresponds to the direction of the line
of sight and that moving in this direction is equivalent to moving in redshift. Since the size of the halo catalogs in the z
direction is smaller than the comoving distance from redshift 5.3 to
8.5 we piled the catalogs in order to cover all the needed distance range but we rotated the upper catalogs in order to not
repeat structures in the line of sight direction.
The initial position of the halos was assumed to be at the comoving distance at which emitted CII
photons are observed at a frequency of 300 GHz (df300). The position (xi,yi,zi) of the halos was
assumed to be at a distance (dx=xi×dr−Lbox/2,
dy=yi×dr−Lbox/2,distz=df300+zi×dr),
where dr=Lbox/Nbox, which corresponds to a comoving distance
distc=(d2x+d2y+d2z)1/2 and to an angular position in right ascension and declination of respectively:

RA=arctan(dxdcom),

(20)

and

DEC=arctan(dydcom).

(21)

Each comoving position was converted first to a redshift and then to an observed frequency using
νobs=νCII/(1+z).
The halos were then distributed in the cone according to their angular position and observed frequency. For each halo
catalog at a redshift z we only used the halos with a redshift lower than z+dz.

In each cell of the mock observing cone, the intensity was assumed to be given by a sum over the contribution from each galaxy as:

ICII=∑i1dfoLCII(M,z)4πD2L.

(22)

5. Simulations of the CO foreground contamination

The CO mock observational cones were made using the following steps:

A dark matter density field with a size of L3halos=2963h−3Mpc3 and a number of cells of
Nhalos=12003 was generated using the Simfast21 code.

The same code was used to generate dark matter halo catalogs from the previously
generated density field using the excursion set formalism and by sampling the halos directly from the density field. These
catalogs were made for redshifts 0 to 2.5 with
a redshift step of 0.1 and a halo mass range of 108M⊙ to 1015M⊙. The halo
properties contained in the catalogs include only the halo mass and position in a three dimensional box with the size
and resolution of the density field.

We randomly assigned astrophysical properties, such as SFR, CO fluxes and visual absolute magnitudes, from the
De Lucia & Blaizot (2007) and the Obreschkow et al. (2009a) simulated galaxy catalogs, to the halos (e.g. we allowed some randomness
in the astrophysical properties for halos with same mass and redshift, using distributions from the SAX simulation).

We calculated the CO luminosity for each halo from its CO flux.

We repeated steps 5 and 6 of the CII signal generation assuming that
the position z=0 of the halos corresponded to
a comoving distance of zero and that the redshift could be converted to an observed frequency using
νobs=νJCO/(1+z).

For each CO transition we built mock observing cones with intensities estimated as in the CII
case and then we added the cones to obtain the total CO intensity.

In order to simulate the effect of the masking technique we made a mock observing cone with only the galaxies with
CO fluxes above a given threshold. The pixels with at least one galaxy correspond to pixels that should be masked in
order to decrease the CO contamination in CII observational maps and so we put to zero the corresponding pixels in the initial
CO box and in the CII box. We also used the same technique with a limit in magnitudes in the AB system K filter (mK)
instead of a limit in CO flux.

A slice of a mock observational CII cone is shown in Figure 9. This figure
shows that CII emission is not randomly distributed but that it follows the underlying density fluctuations.

One of the advantages of simulating mock observational cones is that we can directly add the signal and its contaminants
to obtain a more realistic version of an observational intensity map.
This is useful because it gives us better predictions of what an observational experiment will actually measure and how
to relate the observed signal to the intrinsic signal which is where the scientific information really lies. The analysis of the information contained in these cones is mainly made using the power spectra of the target emission
line and so we used slices in frequency (these slices correspond to the signal emission around a given redshift) from these cones to construct intensity maps in Cartesian coordinates, from which we calculated the signal power spectra.
With this method we directly mapped the contaminants intensity spatial fluctuations into Cartesian coordinates at the signal
redshift. This allowed us to directly obtain a contamination power spectra which is essential to determine the real degree of foreground contamination and to plan ways to clean observational maps.

The CII intensities obtained with these observing cones is shown in Table 7 together with the overall CO
intensity from transitions (2-1) to (6-5) at the same observed frequencies. The results show that CO contamination will
dominate observations especially for low frequencies.

zCII

¯ICII

ImaxCII

IminCII

ICO

8.5

47.0×101

9.50×101

1.80×101

1.05×103

7.5

1.00×102

2.00×102

3.70×101

1.25×103

6.5

1.90×102

3.50×102

7.50×102

1.12×103

5.5

3.36×102

6.00×102

1.33×102

1.06×103

Table 7Intensity of CII emission from galaxies as a function of redshift calculated using the SFR, The medium, maximum
and minimum values of the CII intensity correspond to the LCII versus SFR parameterizations m2, m1
and m4 respectively. Also shown are the CO intensities estimated using the Obreschkow CO model. The intensities
have units of [Jysr−1].

6. Instrument parameters

The characteristics of an experiment able to measure the CII intensity and spatial fluctuations will now be briefly discussed.

Instrument

CII-Stage I

CII-Stage II

Dish size (m)

10

10

Survey area As (arcmin2)

78×0.5

600×600

Instantaneous FOV (arcmin2)

13.6×0.5

25.6×0.4

Freq. range (GHz)

200 - 300

200 - 300

Frequency resolution (GHz)

2

0.4

Number of Spectrometers

32

64

Total number of bolometers

1600

16000

On-sky integration time (hr)

1000

2000

NEFD on sky (mJy√sec)

65

5

Table 8Parameters for a CII experiment

We propose to use one of two similar setups, the first one (CII-Stage I) is appropriate for optimistic CII models (models with a high CII
luminosity density) and the second
one CII-Stage II has the minimum requirements to insure a CII power spectra detection in the case of a more pessimistic CII model.
The choice of a setup for the CII experiment is mainly dependent on the evolution of the CII luminosity for high redshifts and
so it can be updated when more high redshift CII observations are available.

The basic experiment proposed here (CII-Stage I) consists in using one stack of independent single beam, single polarization spectrometers,
one stack for each polarization. Each of these spectrometers would contain several bolometers and each of the
stacks would cover a line on the sky via a polarizing grid. The second stage experimental setup (CII-Stage II) is similar to the first
one but covers a much larger area with a narrower spectra. The details of the proposed experimental setups are shown
in Table 8. The angular resolution of the experiments is (0.5arcmin)2 for CII-Stage I
and (0.4arcmin)2 for CII-Stage II, respectively.

7. Cleaning contamination from lower redshift emission lines

7.1. Pixel masking

As was shown in previous sections, the main line contaminants for the planned observations are CO rotation lines from low redshifts.
Since the contamination from CO emission lines in the CII power spectra is high, we made CO flux cuts to study which galaxies
are dominating the contamination and if they can be removed from the observational data by masking the pixels with the stronger
contaminants.

Figure 10.— AB magnitude in the K filter versus halo mass relation at redshift z=0.06. The relation showed has a small
evolution with redshift. The horizontal lines show what galaxies are being masked according to the mK cuts showed
in figure 11.

Figure 11.— Power spectra of CII emission for four parameterizations of LCII vs SFR (solid lines) and
power spectra of CO contamination (dotted lines) observed in a frequency range of 37GHz centered at
Fobs≈250GHz. The cyan dashed dotted line corresponds to an upper limit for CII emission from ionized regions. Upper left panel corresponds
to the total CII power spectra and CO contamination power spectra.
The middle and right upper panels assume only CO sources with AB relative magnitudes in the K band above mK=22
and mK=23 respectively.
Lower panels assume only CO sources with fluxes below 10−21Wm−2 (left panel), 5×10−22Wm−2
(middle panel) and 2×10−22Wm−2 (right panel). Also shown in the upper left and in the lower panels are
dashed lines of the theoretical CO emission, with the same flux cuts, estimated using the CO observationally based model. The
error bars in the CII models m1 and m4 are based in the experimental setup of the CII-StageII experiment
described in Table 8. Also shown in dashed dotted lines in the top left panel are the errors in the CII models
m1 and m4 based in the experimental setup of the CII-StageI experiment described in Table 8.

Given that detecting galaxies with low CO fluxes
can be very challenging, we also consider using a CO tracer easier to detect such as the SFR or the relative magnitude in a
broad band filter such as the K filter (measured as magnitudes in the AB system in the K filter mK) which is centered at
2190 nm and covers around 390 nm. The
SFR can only be used as a CO tracer in star forming galaxies. Since there is also an intense CO emission in galaxies
powered by active galactic nuclei, if we want to use SFR or infrared emission as a CO tracer we should use an additional
tracer like observations in the visible band to target the active galactic nuclei.

In Figure 10 we can see that galaxies with a high CO flux also have relatively low magnitudes in the
K band. Thus we estimated the mK cut necessary to reduce the power spectra of CO contamination.

We show in the bottom panels of Figure 11 that for the more optimistic CII models the
power spectra of CO contamination can be efficiently reduced by removing from the observational maps contamination by galaxies with CO fluxes
in one of the CO rotation lines higher than 5×10−22Wm−2 and that this can be done by masking less than 10% of
the pixels for an experiment with a setup similar to the CII-Stage II experimental setup. In alternative the top panels of this figure show that masking in mK magnitudes is
also possible and the necessary masking would require a cut of mK=22 in order to sufficiently decrease the power
spectra of CO contamination predicted for a CII model like m2.

For CII models which yield lower intensities the mK cut
would have to be of mK=23 or even higher which would make it impossible to apply the masking technique.
The CO masking can be done with cuts in quantities like the CO flux, SFR, IR luminosity, magnitude in a given band or a
combination of probes depending of the CO tracer experiments available. The masking cuts considered in this study
are presented in Table 9 following the CII-Stage I or CII-Stage II experimental setups and assuming the Obreschkow CO model. The observational
model would require masking CO galaxies till a flux cut of fCO=2×10−22Wm−2 which corresponds to a masking percentage
of 10% or 21% for the CII-Stage II and CII-Stage I experimental setups respectively.

Flux/mK cuts

CII-Stage I

CII-Stage II

Masking %

Masking %

fCO>1×10−21[Wm−2]

7.70

1.97

fCO>5×10−22[Wm−2]

12.99

3.39

fCO>2×10−22[Wm−2]

23.31

6.40

mK<22

6.23

1.58

mK<23

13.76

3.60

Table 9 Masking percentages for an observation in the frequency range from 200 to 300 GHz

If we are able to measure CO luminosities of some galaxies to a high precision it will be possible
to remove their intensity from each pixel instead of masking the pixel completely. This would
reduce the masking percentage. However the number of galaxies
which we can observe with the necessary precision to remove their contamination from observations accurately should be rather small. Also, in order to do this, the
intensity of the galaxy would have to be above the “noise” in each of the pixels.

7.2. Cross correlating foregrounds

In this section we discuss the possibility to use cross correlation as a method to help removing CO foregrounds from
CII maps and as a way to probe the degree of CO contamination remaining in CII maps after the masking technique has
been applied.

7.2.1 Cross correlation with galaxy surveys

First, we consider cross correlating a CO line with the number density of galaxies.

As is shown in Figure
12 the intensity of CO emission in the CO(5-4) line is strongly correlated with the
galaxies number density at the same redshift since they both trace the underlying dark matter
density fluctuations.

Figure 12.— Cross correlation power spectra between number of galaxies and intensity of the CO(5-4)
line at redshift z=1.4 obtained from our simulations. The 1σ uncertainty shown in orange was obtained by cross correlating these two quantities
in different regions of the space.

Here we consider the case that the number density of galaxies is independently measured with a galaxy survey. The number density of
galaxies at a redshift z=1.4 can be cross-correlated with an observational intensity map of the CO(5-4) line centered
at the same redshift (obtained
from the 200 - 300 GHz observing cone) and the result will be proportional to the intensity fluctuations of the CO(5-4) line
even if the intensity map also contains CII and other CO lines.
This can be done for several foreground lines and redshifts to probe the degree of contamination by these lines.

7.2.2 Cross correlation between two CO lines

As can be observed in Table 3, in some cases there are two CO lines originated from the same redshift contaminating
the observational maps at two different frequencies.
For example, the CO(3-2) and the CO(4-3) emitted at a redshift of z=0.6
will be observed at frequencies of 288.2 GHz and 216.1 GHz respectively, and so they will contaminate CII intensity maps at
redshifts 7.8 and 5.6.

Figure 13.— Cross correlation power spectra between observational maps with 70 Mpc centered at frequencies 288.2 GHz and 216.1 GHz
which correspond to CII emission from redshift 7.8 and 5.6. The blue thin lines shows the cross correlation obtained from
maps with only CII emission. The red thick lines shows the cross correlation obtained from maps with CII plus
CO. Solid line denote the full signal while dotted lines denote the signals masked till a CO flux of
2×10−22Wm−2. The masking was done assuming the CII-Stage II experimental setup.

As is shown in Figure 13 the cross correlation between observational maps
with CII plus CO will be stronger than maps with just CII and so by cross correlating intensity maps before and
after masking, we can confirm if the cleaning procedure was successful.
Also, the existence of contamination from two lines emitted from the same redshift can in principle be implemented in algorithms
to help removing the CO contamination, although that task is out of the objectives of this study.

8. Cross correlation between the HI and the CII lines

Both fluctuation in HI and in CII intensity maps are correlated with fluctuations in the underlying density field and so
the spatial distribution of emission in these two lines is correlated. Therefore, the cross correlation power spectra of the
the two lines gives a measure of their intensities.

Since CII is emitted from galaxies and HI is emitted from the IGM these two quantities are mostly negatively correlated
at large scales. At small scales the correlation between CII and HI emission should be positive since they are both biased
in overdense regions. However, we find no correlation in our simulations, which is probably due to the low intensity of 21 cm emission at theses scales.

Figure 14.— Absolute value of the correlation power spectra between CII emission (models m2 and
m3) and the
neutral hydrogen 21 cm line at redshift z=7.0. The error bars were estimated assuming the CII-Stage II experimental setup. Note
that these two lines are negatively correlated at the shown scales.

In Figure 14 we show the cross power spectra between HI emission and two models for CII emission.
The error bars shown in this figure were obtained with the HI 21 cm line experiment described in Table 10 and
with the CII-Stage II instrument.

SKA1-low(z=7)

unit

station diameter Dstat

35

m

survey area As

6.55

deg2

FoV per station

6.55

deg2

effective area per stat. Ae

355.04

m2

freq. resolution dν

3.9

kHz

bandwidth (z=8±0.5) BW

18

MHz

tot. int. time tint

200

hr

min. baseline Dmin

35

m

max. baseline Dmax

1

km

collecting area Acoll

307466

m2

uvmin

21

uvmax

596

Tsys

291

K

effective num. stat.

866

Table 10Parameters for SKA1-low

9. Conclusions

In this paper we consider the possibility of applying the intensity mapping technique to the CII line at high redshifts in
order to probe the EoR and galaxy properties in the early Universe. The ionized carbon CII 158μ m line is one
of the strongest emission lines in the spectra of star forming galaxies and so observing this
line is one of the few possible ways to study very distant galaxies. Given the uncertainty in CII emission from high redshift galaxies
we took into consideration four models for CII emission which cover the uncertainty in the relation between CII emission and SFR. We concluded
that intensity mapping of the CII line during the end of the EoR is in the reach of today’s technology.

The intensity of the CII signal from z∼8.5 to z∼5.5 is likely to be between 102 and 103Jysr−1 although
higher values would be possible if the SFRD is higher than the current predictions.
In the local universe, CII emission from star-forming galaxies is a good probe of their SFR and so intensity mapping of
this line should provide good constraints on the SFRD at high redshifts, even if the constant of proportionality between CII luminosity and SFR
evolves with redshift. Although a reasonable dispersion in the CII emission versus SFR relation is expected, in intensity mapping studies, we are averaging the relation over
thousands galaxies in each pixel, so that the total CII emission should be averaged by the SFRD. The CII intensity should be dominated by galaxies
with luminosities below the threshold of galaxy surveys and so even if CII emission in bright galaxies is not a perfect tracer for star formation,
it should provide good constraints in the SFRD.
The CII line is also dependent in the ISM metallicity and although CII intensity maps cannot give strong constraints to this quantity they will
provide a lower limit which will be on its own an improvement over current constraints of the gas metallicity at high redshifts. Note that
redshift evolution of the metallicity can tell us about the characteristics of POP II and POP III stars
which is also particularly important for Reionization studies.

Emission from CO rotation lines is going to be the main contaminant in CII observations and although the
CO and CII intensities have a large uncertainty it is reasonably confirmed that some of the CO signal has to be removed from
observations in order to recover the correct CII fluctuations.
We estimated the CO intensity using two independent methods, one based in detailed simulations of gas conditions in galaxies
and physical relations between CO transitions and other which uses only observational quantities and observational based relations
between these quantities.
Both these methods predict similar CO intensities.
The current constraints in CO and CII emission indicate that the CO power spectra will be up to one order of magnitude higher
than the CII power spectra. However we showed that the CO signal can be reduced at least as much, by masking the pixels contaminated by the galaxies with the brighter CO emission.

We described an experiment which is within reach of current technology and is able to measure the CII power spectra with
enough resolution so that we can mask most of the CO contamination without erasing the CII signal.
In order to identify the most luminous CO galaxies we propose to use a galaxy survey able to measure CO luminosities or a
more modest survey able to detect the galaxies AB magnitudes in the K band, since this is a good tracer of CO luminosity.
A galaxy survey able to measure CO luminosities of several transitions till a redshift of at least 2.5 would also provide the
first LFs for CO transitions higher than the first CO rotational transition which would by it self be a valuable
contribution to the study of gas conditions of galaxies.

If the CO contamination is too high and the masking technique is not enough to successfully clean the
images or in order to confirm if the contamination was well removed, we can use cross correlations between different
CO lines to estimate the intensity of their contamination.
Even in the worst case scenario where the overall CO emission is a few times higher than what we have considered, we still would be able to remove CO to at
least detect the CII signal with the proposed CII-Stage II experimental setup. Moreover cross correlation between intensity maps of CII and other lines from
the same redshift will not suffer from line contamination.

Finally the CII line and the 21 cm line are expected to be strongly anticorrelated. By cross correlating CII and 21 cm maps,
we will obtain a statistical estimate of the intensity of these signals independent of most foregrounds which can be a valuable
asset in constraining Reionization.

This work was supported by FCT-Portugal with the grant SFRH/BD/51373/2011 for MBS and
under grant PTDC/FIS-AST/2194/2012 for MBS and MGS.
MGS was also supported by the South African Square Kilometre Array Project and the South African National Research Foundation.
AC and YG acknowledge support from NSF CAREER AST-0645427 and AST-1313319 at UCI and also from the Keck Institute for Space Studies (KISS) subcontract for intensity mapping studies.
MBS was also a long Visiting Student at UCI, supported by NSF CAREER AST-0645427 and AST-1313319 and she thanks the Department of Physics and Astronomy at UCI for hospitality during her stay.
We thank Jamie Bock, Matt Bradford and the TIME team for useful discussions.

In this appendix we summarize the key steps necessary to obtain the continuum foregrounds which will contaminate CII intensity maps in the
frequency range 200 - 300 GHz. This study includes contamination by stellar emission, dust emission, free-free and free-bound emission and finally
two photon emission.

.0.1 Stellar emission

The stellar luminosity at frequency ν is approximately given by the emissivity of a black body (Bν) integrated
over the solid angle and the area of the stellar surface (4πR2∗):

L⋆ν=π4πR2∗Bν(Teff∗).

(1)

For estimating the stellar radius (R∗) and for the star effective temperature (Teff) we used the formulas in
(Cooray et al. 2012) for POP II stars and POP III stars.
We calculated separately the emission from POP II and POP III stars assuming that the POP III stellar population
evolution could be described using the error function.
The error function is given by:

fp(z′)=12[1+erf(z−ztσp)],

(2)

where we imposed that the POP III population ended at z=6, that POP III stars are the dominant population
for zt≥10 and that the POP III transition width is σP=0.5. A discussion for the
choice of these values can be found at (Fernandez & Zaroubi 2013).

The observed stellar luminosity density is the sum of the luminosity density of POP II stars (lPOPII)
and of POP III stars (lPOPIII) given respectively by:

We integrated in stellar mass using a (Salpeter 1955) IMF (Initial Mass Function) with a
mass range from 0.1 to 100 M\sun for POP II stars and a (Larson 1998) IMF with a mass
range from 0.1 to 500 M\sun, and Mc∗=250M\sun for POP III stars.
In Equations 3 and 4, Mcut(z,z′), corresponds to the maximum stellar
mass of a star created at redshift z′ which is still alive at z and K(z′) is the normalization of the mass
function in units of [Mpc−3s−1] so that the total stellar mass coincides with the value that can be
obtain with the star formation rate density Ψ in units of M⊙Mpc−3s−1.
For POP II and POP III stars K(z′) is given respectively by:

K(z′)

=

Ψ(z′)fp(z′)∫Mmax∗Mmin∗M−2.35∗M∗dM′∗

(5)

and

K(z′)

=

Ψ(z′)[1−fp(z′)]∫Mmax∗Mmin∗M−1∗(1+M∗Mc∗)−1.35M∗dM′∗

(6)

The stellar emission contamination to the observed frequency νo is given by: